Apparatus and methods for determining isotropic and anisotropic formation resistivity in the presence of invasion

ABSTRACT

A logging tool includes a tool body; a simple transmitter comprising a single antenna disposed on the tool body; four simple receivers, each comprising a single antenna, disposed on the tool body and spaced apart from the simple transmitter to form four arrays; and an electronic module for controlling operation of the four arrays, wherein the simple transmitter is configured to generate a magnetic field having a transverse component, wherein each of the four simple receivers is sensitive to the magnetic field generated by the simple transmitter, and at least one of the four simple receivers is sensitive to the transverse component of the magnetic field generated by the simple transmitter, and wherein the four arrays are configured to provide measurements at at least three depths of investigation.

CROSS REFERENCE TO RELATED APPLICATIONS

This claims priority to U.S. Provisional Patent Application Ser. No.60/514,720, filed on Oct. 27, 2003. This Provisional Application isincorporated by reference in its entirety.

BACKGROUND OF INVENTION

1. Field of the Invention

The invention relates generally to the field of well logging. Moreparticularly, the invention relates to tools and methods for measuringelectrical properties of a formation with anisotropy and/or invasion.

2. Background Art

Induction tools have been used for many years to measure the resistivityof earth formations surrounding a borehole in the presence of boreholefluids that may have invaded the formations. Induction logging toolsmeasure the resistivity (or its inverse, conductivity) of the formationby inducing eddy currents in the formations in response to an ACtransmitter signal. The eddy currents induce secondary magnetic fieldsthat in turn induce voltages in receiver antennas. Because themagnitudes of the eddy currents depend on formation conductivities, themagnitudes of the received signals thus reflect the formationconductivities.

A typical induction tool includes at least two induction arrays havingdifferent spacings between the transmitters and the receivers fordifferent depths of investigation (DOI). An example of such tools isdisclosed in U.S. Pat. No. 3,067,383 issued to Tanguy. A minimalconfiguration of such tools includes two coil arrays for measuring attwo different DOI: a deep array (ILD) and a medium array (ILM). The deeparray is designed to “see” beyond the mud invaded zone in order toprovide true formation resistivity (R_(t)). However, in order todetermine the minimum parameters (the invaded zone resistivity, R_(xo),the resistivity of the uninvaded zone, R_(t), and the radius ofinvasion, r_(i)) of a formation invaded by drilling fluids, at leastthree measurements at different depths of investigation are required.Historically, the third measurement (a shallow measurement) is providedby a focused electrode array. One such tool is disclosed in U.S. Pat.No. 3,329,889 issued to Tanguy. The shallow electrode measurementtogether with the medium (ILM) and deep (ILD) measurements provided bythe induction arrays provide sufficient data to solve formationresistivities in a formation with a simple invasion profile. Such toolsmay not provide sufficient data for the determination of formationproperties when the invasion profiles is complicated, e.g., more thanone zone surrounding the borehole with different resistivities.

Therefore, multi-array tools have been introduced for the determinationof formation resistivity in formations with more complex invasionprofiles. Examples of multi-array tools include those disclosed in Hunkaet al., “A New Resistivity Measurement System for Deep Formation Imagingand High-resolution Formation Evaluation, ” Paper SPE 20559, presentedat the 65^(th) SPE Annual Technical Conference and Exhibition, NewOrleans, La., Sep. 23–26, 1990, and U.S. Pat. No. 5,157,605 issued toChandler et al. The multiple arrays, having different spacings betweenthe transmitter and the receiver, can provide measurements at differentdepths of investigation (DOI). Therefore, when mud invasion occurs todifferent extents (radii) in different layers, sufficient data may stillbe provided by such tools for solving formation electrical properties.

In addition to mud invasion, formation anisotropy can also complicateresistivity logging and interpretation. Formation anisotropy resultsfrom the manner in which formation beds were deposited by nature.Formations containing hydrocarbons often exhibit anisotropy in formationresistivity. In such formations, the horizontal conductivity, σ_(h), (orresistivity, R_(h)) in a direction parallel to the bedding plane differsfrom the vertical conductivity, σ_(v), (or resistivity, R_(v)) in adirection perpendicular to the bedding plane. In crossbedded reservoirs,the anisotropic resistivities may be better defined in two directionsother than those that are parallel and perpendicular to the formationlayers. For clarity of illustration, this description uses “horizontal”and “vertical” in a broad sense to describe the two orthogonaldirections of the anisotropic resistivities, regardless of whether thesedirections are actually parallel or perpendicular to the bedding planes.The actual directions can be resolved by the inversion methods used inlog analysis, for example the method to be described in FIG. 9.

Conventional induction logging tools, such as those described above,have their transmitters and receivers arranged in a manner such thattheir magnetic dipoles are aligned with the longitudinal axis of thetools. These longitudinal induction array tools induce eddy currents inloops that are perpendicular to the longitudinal axes of the tools.Therefore, these tools are sensitive only to the horizontal conductivityof the formations; they cannot provide a measure of verticalconductivity (or resistivity) or anisotropy.

To measure the vertical conductivity or anisotropy, new EM induction orpropagation instruments typically include transmitter and/or receiverantennas that have their magnetic dipoles substantially perpendicular tothe axis of the instrument. These tools with transverse induction arrayshave good sensitivity to formation resistivity anisotropy. See e.g.,Moran and Gianzero, “Effects of Formation Anisotropy on ResistivityLogging Measurements, ” Geophysics, 44, 1266–1286 (1979). Transverseinduction arrays tools include triaxial array tools, which include threeorthogonal transmitter coils and three receivers coils in the sameorthogonal orientations. In operation, the tri-axial transmitter isenergized in three orthogonal directions. Individual receiver coilsaligned in the same three orthogonal directions then measure thevoltages induced by eddy currents flowing in the surrounding formations.Examples of triaxial tools, for example, may be found in U.S. Pat. No.3,510,757 issued to Huston, U.S. Pat. No. 5,781,436 issued to Forgang etal., U.S. Pat. No. 3,609,521, issued to Desbrandes, U.S. Pat. No.4,360,777, issued to Segesman, and U.S. Pat. No. 6,553,314 issued toKriegshäuser, et al. These triaxial array induction tools can determinethe formation anisotropic resistivity as long as the formation isuninvaded or the invasion depth is shallow.

Although certain prior art tools are capable of measuring resistivitiesof formations with complex invasion profiles and others are good forformations with anisotropy, prior knowledge of the formation type isneeded in order to choose a proper tool. It is desirable that EMinduction or propagation logging tools are available to provide reliablemeasurements of formation resistivities without prior knowledge offormation anisotropy and/or invasion.

SUMMARY OF INVENTION

In one aspect, embodiments of the invention relate to logging tools. Alogging tool in accordance with one embodiment of the invention includesa tool body; a simple transmitter comprising a single antenna disposedon the tool body; four simple receivers, each comprising a singleantenna, disposed on the tool body and spaced apart from the simpletransmitter to form four arrays; and an electronic module forcontrolling operation of the four arrays, wherein the simple transmitteris configured to generate a magnetic field having a transversecomponent, wherein each of the four simple receivers is sensitive to themagnetic field generated by the simple transmitter, and at least one ofthe four simple receivers is sensitive to the transverse component ofthe magnetic field generated by the simple transmitter, and wherein thefour arrays are configured to provide measurements at at least threedepths of investigation.

A logging tool in accordance with another embodiment of the inventionincludes a tool body; a transmitter comprising two antennas disposed onthe tool body, wherein the two antennas are arranged in differentorientations; two simple receivers, each comprising a single antenna,disposed on the tool body and spaced apart from the transmitter; a thirdreceiver, comprising two antennas, disposed on the tool body and spacedapart from the transmitter and the two simple receivers; and anelectronic module for controlling operation of four arrays formed by thetransmitter and the two simple receivers and the third receiver, whereinat least one of the two antennas in the transmitter is configured togenerate a magnetic field having a transverse component, wherein atleast one of the two antennas in the third receiver is responsive to thetransverse component of the magnetic field generated by the transmitter,and wherein the four arrays are configured to provide measurements at atleast three depths of investigation.

A logging tool in accordance with another embodiment of the inventionincludes a tool body; a transmitter comprising three antennas disposedon the tool body, wherein the three antennas are arranged in threedifferent directions; two simple receivers, each comprising a singleantenna, disposed on the tool body, wherein each of the two simplereceivers is spaced apart from the transmitter; a third receiverdisposed on the tool body and spaced apart from the transmitter and thetwo simple receivers, wherein the third receiver comprises threeantennas arrange in three directions substantially identical to thethree different directions of the three antennas of the transmitter; andan electronic module for controlling operation of the transmitter, thetwo simple receivers, and the third receiver, wherein arrays formed bythe transmitter and the two simple receivers and the third receiver areconfigured to provide measurements at at least three depths ofinvestigation.

A logging tool in accordance with another embodiment of the inventionincludes a tool body; a transmitter disposed on the tool body, whereinthe transmitter is configured to generate a magnetic field having atransverse component; four receivers disposed on the tool body andspaced apart from the transmitter; and an electronic module forcontrolling operation of the transmitter and the four receivers, whereineach of the four receivers is responsive to the magnetic field generatedby the transmitter, wherein at least one of the four receivers isresponsive to the transverse component of the magnetic field generatedby the transmitter, and wherein arrays formed by the transmitter and thefour receivers provides at least three depths of investigation.

In another aspect, embodiments of the invention relate to a method forwell logging. A method for well logging in accordance with oneembodiment of the invention includes disposing a logging tool in aborehole penetrating a formation; obtaining a plurality of measurementsof formation resistivity, wherein the plurality of measurements cover atleast three different depths of investigation and at least one of theplurality of measurements is sensitive to formation anisotropy; anddetermining an electrical property of the formation based on theplurality of measurements.

Other aspects and advantages of the invention will be apparent from thefollowing description and the appended claims.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows a prior art logging system.

FIG. 2 shows a logging tool in accordance with one embodiment of theinvention.

FIG. 3 illustrates a triaxial antenna array including a triaxialtransmitter, a triaxial bucking receiver, and a triaxial receiver.

FIG. 4 shows a radial responses of the tool shown in FIG. 2 inaccordance with one embodiment of the invention.

FIG. 5 shows a effects of mud invasion and anisotropy on the real (R)and quadrature (X) signals as acquired by a 72 inch triaxial array.

FIG. 6 shows a logging tool in accordance with one embodiment of theinvention.

FIG. 7 shows a radial responses of the tool shown in FIG. 6 inaccordance with one embodiment of the invention.

FIG. 8 shows a logging tool in accordance with one embodiment of theinvention.

FIG. 9 shows a method for deriving formation resistivity from log dataacquired using a tool in accordance with one embodiment of theinvention.

FIG. 10 shows a 1D formation model that may be used with a method inaccordance with one embodiment of the invention.

FIG. 11 shows a 2D formation model that may be used with a method inaccordance with one embodiment of the invention.

FIG. 12 shows a 3D formation model that may be used with a method inaccordance with one embodiment of the invention.

FIG. 13 shows a schematic illustrating an axial and a transversecomponent of a magnetic moment of a tilted antenna.

DETAILED DESCRIPTION

Embodiments of the present invention relate to apparatus and methods fordetermining electrical properties of a formation having mud invasionand/or anisotropy. To solve the electrical properties (R_(xo), r_(i),and R_(t)) of a formation with invasion, three measurements at differentDOIs are required. If the formation also has anisotropy, then oneadditional measurement that is sensitive to anisotropy is required(e.g., a transverse measurement). Therefore, a minimum of fourmeasurements are required for solving a formation with invasion andanisotropy. These four measurements should be acquired at at least threedifferent DOIs for three of the measurements, and at least one of thefour measurements should be sensitive to formation anisotrophy. The fourmeasurements may be any of the following combinations: (1) three axialmeasurements and one transverse measurement; (2) two axial measurementsand two transverse measurements; (3) one axial measurement and threetransverse measurements; and (4) four transverse measurements.

As used herein, “axial” means a direction parallel with the longitudinalaxis of the tool, and “transverse” means a direction perpendicular tothe longitudinal axis of the tool. Thus, an “axial” antenna (transmitteror receiver) refers to a coil having a magnetic moment parallel with thelongitudinal axis of the tool, while a “transverse” antenna (transmitteror receiver) refers to a coil having a magnetic moment perpendicular tothe longitudinal axis of the tool. A tilted antenna has a magneticmoment that is neither perpendicular nor parallel to the longitudinalaxis of the tool. However, the magnetic moment of a tilted antenna canbe decomposed into an axial component and a transverse component (seeFIG. 13). In other words, the magnetic field generated by a tiltedantenna includes a transverse component and an axial component.Embodiments of the invention may require the use of an axial receiver ora transverse receiver. In these cases, a tilted antenna may be usedinstead to provide the axial component or the transverse component.Therefore, a general term “axial-component” receiver is used in thisdescription to refer to a receiver having a magnetic moment thatincludes a component in the axial direction, and “transverse-component”receiver is used to refer to a receiver having a magnetic moment thatincludes a component in the transverse direction. Thus, an“axial-component” receiver may include an axial antenna or a tiltedantenna, and a “transverse-component” receiver may include a transverseantenna, a tilted antenna, or a triaxial antenna. A transmitter and areceiver form an array. In some embodiments, an array further includes abucking receiver to reduce or remove the mutual couplings between thetransmitter and the receiver. Thus, an “axial-component” array refers toan array that includes a transmitter and a receiver, each having amagnetic moment including a component in the axial direction, and a“transverse-component” array refers to an array that includes atransmitter and a receiver, each having a magnetic moment including acomponent in the transverse direction.

Accordingly, an axial measurement may be acquired with an axial array oran axial-component array, and a transverse measurement may be acquiredwith a transverse array or a transverse-component array. For example, ameasurement acquired using a tilted array may be decomposed into anaxial component measurement and a transverse component measurement.

As will be described later, any of the axial arrays (or axial-componentarrays) in a tool of the invention may be replaced with an electrodedevice. Therefore, any or all of the axial measurements described abovemay be replaced with electrode (galvanic) measurements. Embodiments ofthe invention may use any electrodes device known in the art, includingbutton electrodes, ring electrodes, and toroid electrodes. One ofordinary skill in the art would appreciate that an electrode deviceincludes a current injector and a sensor for detecting currents thatflow back to the tool. In this description, an “electrode” is used in ageneral sense to refer to an electrode device and is not limited to anyparticular type of electrode device. Note that four measurementsrepresent a minimum requirement for solving electrical properties of aformation with a simple invasion profile (e.g., a single invaded zonewith a constant resistivity) and a simple anisotropy (e.g., thedirection of anisotropy is known). In a formation with more complicatedinvasion and/or anisotropy, more measurements will be required.

Thus, a resistivity logging tool in accordance with embodiments of theinvention can provide at least four measurements, which include at leastthree measurements at different DOIs and at least one measurement thatis sensitive to anisotropy. Several tool configurations are capable ofproviding these measurements. A simple tool configuration, for example,may comprise a common transmitter, three axial-component receivers, anda transverse-component receiver. Each receiver and the commontransmitter from an array. Therefore, this simple tool configurationincludes three axial-component arrays and one transverse-componentarray. Because the common transmitter needs to work in theaxial-component arrays and the transverse-component array, it mayinclude two coils—an axial coil (antenna) and a transverse coil.Alternatively, the transmitter may be a tilted antenna, which includesan axial component and a transverse component in the magnetic moment.Note that the common transmitter may also be a triaxial antenna. Themagnetic moment of the transverse component in the transmitterpreferably is preferably in the same direction as the magnetic moment ofthe transverse receiver; however, they may form an angle (other than90°—i.e., not orthogonal) when projected onto a transverse plane. Atransverse plane is a plane perpendicular to the longitudinal axis ofthe tool.

A “triaxial” antenna (transmitter or receiver) in this description isused in a broad sense to mean three antennas arranged in threenon-coplanar directions, which may or may not be orthogonal to eachother. If these antennas are not orthogonal to each other, theirmagnetic moments can be resolved into three orthogonal components. Inpreferred embodiments, the three antennas in a triaxial transmitter orreceiver are arranged in orthogonal orientations. In more preferredembodiments, one of the three orthogonal antennas in the triaxialtransmitter or receiver is in a direction substantially aligned with thelongitudinal axis of the tool. In this case, the triaxial transmitter orreceiver includes a longitudinal antenna and two transverse antennas.

While preferred embodiments of this invention involve the use oftriaxial transmitters and receivers, in some cases, only transverse ortilted transmitters and receivers are necessary. For example, if thedirection of anisotropy is unknown, then full triaxial measurements maybe necessary. On the other hand, in a simple case where the direction ofanisotropy is known, it is only necessary to have transversemeasurements. In this description, “transmitter” and “receiver” are usedto describe different functions of an antenna/coil, as if there weredifferent types of coils. This is only for clarity of illustration. Atransmitter coil and a receiver coil have the same physicalcharacteristics, and one of ordinary skill in the art would appreciatethat the principle of reciprocity applies and an antenna/coil may beused as a transmitter at one time and as a receiver at another. Thus,any specific description of transmitters and receivers in a tool shouldbe construed to include the complementary configuration, in which the“transmitters” and the “receivers” are switched. Furthermore, in thisdescription, a “transmitter” or a “receiver” is used in a general senseand may include a single coil, two coils, or three coils. If a singlecoil “transmitter” or “receiver” is desired, it will be referred to as a“simple transmitter” or a “simple receiver.”

FIG. 1 shows a schematic of a typical logging system. Certainconventional details are omitted in FIG. 1 for clarity of illustration.The logging system 100 includes a logging tool 105 adapted to bemoveable through a borehole. The logging tool 105 is connected to asurface equipment 110 via a wireline 115 (or drill string). Although awireline tool is shown, those skilled in the art would appreciate thatembodiments of the invention may be implemented in wireline orwhile-drilling (LWD or MWD) operations. The surface equipment 110 mayinclude a computer. In accordance with embodiments of the invention, thelogging tool 105 is equipped with at least three antenna arrays fordetermining formation resistivity in the presence of invasion and/oranisotropy.

As noted above, to determine electrical properties of a formation thatis radially inhomogeneous (e.g., invaded by drilling fluids orinherently inhomogeneous), measurements at multiple (e.g., three) depthsof investigation (DOI) are required. A tool in accordance withembodiments of the invention may include a plurality of antenna arraysto provide at least three measurements at different DOIs and at leastone measurement that is sensitive to anisotropy. Most of the pluralityof antenna arrays may be axial arrays. However, at least one of themshould be an array having a transverse component, i.e., a triaxial,tilted, or transverse array. For clarity, the following description mayuse triaxial arrays (transmitters or receivers) to illustrateembodiments of the invention. One of ordinary skill in the art wouldappreciate that other transmitters or receivers having transversecomponents (e.g., tilted or transverse transmitters or receivers) may beused in the place of the triaxial transmitter or receivers.

In accordance with one embodiment of the invention, a logging toolincludes at least three antenna arrays and at least one of the at leastthree antenna arrays is responsive to the transverse component of themagnetic field generated by the transmitter (e.g., a triaxial, tilted,or transverse array). The at least one triaxial, tilted, or transversearray provides measurements that can be used to derive anisotropicproperties of the formation, i.e., R_(h), R_(v), and anisotropycoefficient (λ). One example of such a tool is shown in FIG. 2.

FIG. 2 shows an induction or propagation tool 200. Note that embodimentsof the invention may be used as an induction tool or a propagation tool.Because the difference between these two types of tools is not germaneto the present invention, the following description uses “induction”tools in a general sense to refer to both “induction” and “propagation”tools. As shown, the induction tool 200 includes an electronic module201 and a mandrel 202, on which a series of antennas are disposed. Theelectronic module 201 includes components for controlling the signals toenergize the transmitter and for controlling the acquisition of thesignals (voltages) by the receivers. In addition, the electronic modulemay include a processor and/or a memory. The memory may store a programfor performing the logging operation and data processing. The tool 200also includes a protective housing (not shown) disposed over the variousantennas. The induction tool 200 includes a triaxial transmitter 210T,two axial receivers, 221 m and 222 m, and one triaxial receiver, 231 m.Each of the receivers is coupled with a corresponding bucking receiver,221 b, 222 b, and 231 b, respectively. In the notation, suffix “b”indicates that the antenna (coil) functions as a bucking receiver, andsuffix “m” indicates that the antenna (coil) functions as a mainreceiver antenna. The function of a bucking receiver is to reduce orremove mutual couplings between the transmitter and the receiver.

The common triaxial transmitter 210T, the two axial receivers, 221 m and222 m, and the two bucking receivers, 221 b and 222 b, together form twoaxial arrays, while the common triaxial transmitter 210T, the triaxialreceiver 231 m, and the triaxial bucking receiver 231 b together form atriaxial array. As note above, a “triaxial” transmitter or receiverincludes three coils having their magnetic moments oriented innon-coplanar directions, including orthogonal directions. Furthermore,the “triaxial” transmitter or receiver in this example may be replacedwith a tilted transmitter or receiver. An array, whether axial ortriaxial, includes a transmitter and a receiver. In preferredembodiments, an array further includes a bucking coil/receiver. In thisdescription, “bucking receiver” is used to refer to bucking coils ingeneral e.g., a single-coil (axial) or three-coil (triaxial) buckingreceiver. For an axial receiver, the bucking receiver comprises an axialcoil wound in a direction opposite to the winding direction of thereceiver coil. For a triaxial receiver, the bucking receiver (i.e., atriaxial bucking receiver) consists of three coils wound in the sameorientations as those of the corresponding receiver coils, but inopposite directions.

FIG. 3 shows a schematic of an exemplary triaxial array 300 thatincludes a triaxial transmitter 301, a triaxial bucking receiver 302,and a triaxial receiver 303. Although co-located coils are shown, one ofordinary skill in the art would appreciate that embodiments of theinvention do not require the triaxial antennas to be co-located.Co-location means that the centers of the three coils are substantiallyat the same location. The triaxial transmitter 301 includes three coilshaving their magnetic dipoles (M_(x) ^(T), M_(y) ^(T) and M_(z) ^(T))oriented in orthogonal directions (x, y, z). The triaxial receiver 303includes three coils having their magnetic dipoles (M_(x) ^(R), M_(y)^(R) and M_(z) ^(R)) oriented in the same orthogonal directions (x, y,z). The triaxial bucking receiver 302 includes three coils having theirmagnetic dipoles (M_(x) ^(B), M_(y) ^(B) and M_(z) ^(B)) oriented inorthogonal directions that are in opposite directions (−x, −y, z) tothose of the transmitter 301 and the receiver 303. One of ordinary skillin the art would appreciate that the bucking receiver should be placedbetween the transmitter and the receiver. As shown, the bucking receiver302 is disposed at a distance L_(B) from the transmitter 301. Thedistance L_(B) is shorter than the distance (L_(R)) between thetransmitter 301 and the receiver 303. One skilled in the art willrecognize that a triaxial array for embodiments of the invention neednot be an “orthogonal” triaxial array. Furthermore, more complicatedarrangements using multiple transmitter and or multiple receiver coilsare also possible, both for axial and for triaxial induction arrays.

The precise location and the number of turns of the bucking coil shouldbe selected to maximize the cancellation of the mutual couplings betweenthe transmitter and the receiver. An example disclosed in U.S. Pat. No.5,157,605 includes a bucking receiver disposed at the mid point betweena transmitter and a receiver. In this configuration, the number of turnsof the conductive wire in the bucking coil is ⅛ that of the receivercoil.

The induction tool 200 shown in FIG. 2 includes two axial arrays and onetriaxial array. This represents an example of an induction tool that iscapable of providing resistivity estimates for formations with invasionand anisotropy. In operation, the triaxial transmitter 210T is energizedby passing an alternating current signal therethrough and the voltagesreceived by the receiver in each array are recorded. The three antennasin the triaxial transmitter may be energized at different times (timemultiplexing) or at different frequencies (frequency multiplexing) sothat the responses recorded by the receivers may be differentiated.

In addition to time multiplexing or frequency multiplexing for signalidentification, the triaxial transmitter 110T is preferably operated atmore than one frequency to provide more than one set of measurements fordata processing. The measurements from two or more frequencies, forexample, may be used to reduce the skin effects and/or to focus the DOIas disclosed in U.S. Pat. No. 5,157,605 issued to Chandler et al. Thispatent is assigned to the assignee of the present invention and isincorporated by reference in its entirety. The operating frequency ispreferably in the range of 5 to 200 KHz for induction tools. In someembodiments, an induction tool in accordance with the invention areoperated at two frequencies, e.g., about 26 kHz and about 13 kHz. Thelower frequency (relative to the conventional induction tools that maybe operated at a frequency up to several hundred kHz) is desirablebecause of the greater skin effect on the transverse antennas or arrays.For propagation tools, the operating frequency is preferably in therange of 100 kHz to 2 MHz. In some preferred embodiments, thepropagation tools are operated at two frequencies, e.g., about 400 kHzand about 2 MHz.

The receivers in these arrays are disposed at different distances fromthe common triaxial transmitter 110T. The different spacings (L1, L2,and L3) between the transmitter and the receivers provide differentdepths of investigation (DOI), i.e., different distances into theformation from the wellbore. Because skin effects are a function oftransmitter frequencies in EM logging, it is possible to achievedifferent DOIs by varying the operating frequencies of the transmitters,instead of different transmitter-receiver spacings. In some embodimentsof the invention, different DOIs are accomplished by operating theaxial, transverse or triaxial arrays at multiple frequencies. The depthof investigation of an induction or propagation array is normallydefined as the midpoint of the integrated radial response. One ofordinary skill in the art would appreciate that the radial response ofan array depends on the spacing between the transmitter and thereceiver, among other factors.

FIG. 4 shows the radial geometrical factors of the various arrays in thetool 200 of FIG. 2. Curves 421 and 422 represent the geometrical factorsof the two axial receivers 221 m and 222 m, respectively, while curves431 a and 431 t represent the axial component and the transversecomponent, respectively, of the triaxial receiver 231 m. It is apparentthat the short arrays (axial arrays) have larger responses in the nearwellbore regions. The measurements from the short arrays can be used tocorrect for borehole effects and/or to derive the resistivity in theinvaded zone. The long array (triaxial array) is more responsive to theformation regions farther away from the wellbore (see curves 431 a and431 t). The axial component (curve 431 a) can be combined with the twoaxial measurements to derive formation resistivity properties (R_(xo),r_(i), and R_(t)) in an isotropic formation. In an anisotropicformation, the transverse component (curve 431 t) may be included toprovide the horizontal resistivity (R_(h)), vertical resistivity (R),and anisotropy coefficient (λ). Thus, tool 200 is capable of providingreliable resistivity estimates of a formation regardless of mud invasionand/or anisotropy.

FIG. 2 shows an example of a tool configuration in accordance withembodiments of the invention. One of ordinary skill in the art wouldappreciate that other modifications are possible. For example, the toolmay include a third axial array so that the three different DOImeasurements required to solve the invasion profile do not rely on theaxial component of the triaxial array. Another tool configuration mayinclude a single transverse or triaxial array and a single axial array,such as the tool 200 of FIG. 2 without the bucking receiver 222 b andthe main receiver 222 m. In this case, different operating frequenciesmay be used to obtain measurements at different DOIs. In FIG. 2, thefirst axial receiver 221 m and the second bucking receiver 222 b areshown to be co-wound at the same location on the mandrel 202. In someembodiments, these coils may not be co-wound and may be arranged atdifferent axial locations along the mandrel 202. Furthermore, one of theaxial arrays (e.g., the one including receiver 221 m) may be replacedwith an electrode device to provide the near wellbore resistivitymeasurements. It is known that in some situations (e.g., rugoseboreholes or very high resistivity contrasts between conductive boreholefluids and resistive formations), electrode devices can provide morerobust measurements than an induction array can.

The tool shown in FIG. 2 can provide sufficient measurements todetermine the electrical properties of a formation in which the invasionzone is isotropic. Mud filtrate invasion may render the invaded zoneisotropic in an anisotropic formation. However, if invasion does notremove the anisotropy, then the horizontal (R_(xo,h)) and vertical(R_(xo,v)) resistivities in the invaded zone will be different. FIG. 5shows that anisotropy remains detectable even when invasion zoneadvances 100 inches or more into the formation. The results shown inFIG. 5 are from a simulation of the xx transverse signals with the samespacings as the 72-inch array of an array induction tool sold under thetrade name of AIT™ by Schlumberger Technology Corporation (Houston,Tex.). The formation has a horizontal conductivity (σ_(h)) of 1,000 mS/mand the invaded zone has a conductivity (σ_(xo)) of 100 mS/m. Fiveconditions with R_(v)/R_(h)=1, 2, 5, 10, and 50 are simulated, and boththe in-phase phase signals (σ-R) and the quadrature signals (σ-X) arepresented as a function of the invasion radius.

FIG. 5 clearly shows that the invasion does not completely remove thesensitivity to formation anisotropy even with the invasion reachingbeyond 100 inches. For example, curves 51R and 51X, which represent thein-phase (σ-R) and the quadrature (σ-X) signals for R_(v)/R_(h)=1, arevery different from curves 52R and 52X, which represent the in-phase(σ-R) and the quadrature (σ-X) signals for R_(v)/R_(h)=2. These resultsclearly show that anisotropy can remain in the invaded zone, and thecommon assumption that the invaded zone can be characterized with anisotropic resistivity (R_(xo)) may not be valid.

Thus, in order to fully characterize the formation properties,regardless of invasion or anisotropy, more than one transverse ortriaxial array may be needed. FIG. 6 shows another induction orpropagation tool according to embodiments of the invention. Theinduction tool 600 includes two axial arrays and six triaxial arrays,i.e., five more triaxial arrays than the induction tool 200 of FIG. 2.The induction or propagation tool 600 includes an electronic module 601and a mandrel 602, on which a series of antennas are disposed. Theinduction or propagation tool 600 also includes a protective housing(not shown) disposed over the various antennas. The two axial arraysinclude the common triaxial transmitter 610T, three bucking receivers621 b, 622 b, and three axial receivers 621 m, 622 m, while the sixtriaxial arrays include the common triaxial transmitter 610T, sixbucking receivers 631 b 636 b, and six triaxial receivers 631 m 636 m.This embodiment includes two axial arrays. Thus, an axial component ofone of the triaxial arrays is used to provide the third axialmeasurement, which together with the other two sets of axialmeasurements obtained by the two axial arrays provide measurements atthree different DOIs for determining the invasion profile.

As shown in FIG. 6, the bucking receiver 622 b is co-wound with thereceiver 621 m. Similarly, the six triaxial arrays comprise a series ofco-wound bucking and receiver antennas. These co-wound antennas are forillustration only. Embodiments of the invention may use co-wound ornon-co-wound antennas. If the bucking receiver of one array and the mainreceiver coil of a shorter array are co-wound, they may be co-wound on abobbin that is made of ceramic or any suitable material. In the co-woundconfiguration, the arrays are arranged so that the main receiver coil ofarray n is at approximately the same axial location as themutual-balancing (bucking) coil of array n+1. For example, the buckingreceiver 623 b for the main receiver 623 m is co-wound with mainreceiver 622 m on the same bobbin in FIG. 6. U.S. Pat. No. 5,668,475issued to Orban et al. includes detailed description of co-woundbucking-main receiver coils. This patent is assigned to the assignee ofthe present invention and is incorporated by reference in its entirety.

One of ordinary skill in the art would appreciate that the spacings ofvarious axial arrays and triaxial arrays may be selected to provide thedesired depth of investigation (DOI). An example of the various spacingsis shown in FIG. 6, in which the receivers in the two axial arrays arearranged at 6 and 9 inches from the common triaxial transmitter 310T,and the receivers in the six triaxial arrays are arranged at 15, 21, 27,39, 54, and 72 inches from the common triaxial transmitter 310T. Notethat this is only an example. One of ordinary skill in the art wouldappreciate that these spacings may be varied to obtained the desiredDOIs. Furthermore, the relative positions of the transmitter and thetraixial and axial receivers may be changed. That is, the transmitterneed not be at the top of the tool section (tool body), and the triaxialreceivers need not be at longer spacings from the transmitter than theaxial receivers.

The shorter spacings (6 and 9 inches) of the axial arrays (short arrays)allow these short arrays to measure resistivity close to the borehole,as evidence by their radial geometrical factors (curves 721, 722) shownin FIG. 7. The near wellbore measurements may be used to correctborehole effects in measurements made by long arrays. In addition, theshort array measurements may be used to derive the resistivity of theinvaded zones, R_(xo). Furthermore, the couplings between the transversecoils of the transmitter and the axial coils of the shorter arrayreceivers can provide information concerning borehole size and theposition of the tool in the borehole which is very useful in correctingfor borehole effects.

The triaxial arrays, being at longer spacings, are designed toinvestigate at different distances into the formation, as evidenced bytheir radial geometrical factors (curves 731 736) shown in FIG. 7.Having triaxial measurements at a series of radial distances from theborehole makes it possible to derive the anisotropic resistivities inboth the invaded and uninvaded zones. Thus, the induction or propagationtool 600 shown in FIG. 6 is capable of providing reliable formationresistivity measurements regardless of invasion and/or anisotropy.

As noted above, a tool configuration according to some embodiments ofthe invention includes three arrays, at least one of which is responsiveto the transverse component of the magnetic field generated by thetransmitter (e.g., a tilted or triaxial array). One example is shown inFIG. 2. FIG. 6 shows an induction or propagation tool 600 that includesadditional triaxial arrays as compared with tool 200 in FIG. 2. In asimilar manner, additional axial arrays may be added to theconfiguration of tool 200 in FIG. 2. One such example is shown in FIG.8.

FIG. 8 shows an induction or propagation tool 800 that includes anelectronic module 801 and a mandrel 802, on which antenna arrays aredisposed. A protective housing (not shown) is also included for theprotection of the antenna arrays. As shown, the induction or propagationtool 800 includes seven axial arrays and one triaxial arrays. That is,the induction or propagation tool 800 includes five additional axialarrays, as compared with the tool 200 shown in FIG. 2. The additionalaxial arrays can provide more robust measurements to define theinvasions zones, even if the invasion radius is different in each layer.Thus, tool 800 can be used to measure electrical properties offormations with complex invasion profiles.

The EM induction or propagation tools shown in FIGS. 2, 6, and 8 are forillustrations only. One of ordinary skill in the art would appreciatethat other modifications are possible without departing from the scopeof the invention. In addition, one of ordinary skill in the art wouldappreciate that a tool of the invention may be used in wireline,logging-while-drilling (LWD), or measurement-while-drilling (MWD)operations. Furthermore, these tools may be used in boreholes drilledwith water-based mud or oil-based mud.

In operation, each antenna in the transmitter is energized and theresponse in each receiver is recorded. The measurements from a triaxialarray therefore consist of nine possible couplings between thetransmitter antennas and the receiver antennas. The voltage measurementsthus obtained may be represented as a 3×3 matrix shown in equation (1):

$\begin{matrix}\begin{bmatrix}V_{xx} & V_{xy} & V_{xz} \\V_{yx} & V_{yy} & V_{yz} \\V_{zx} & V_{zy} & V_{zz}\end{bmatrix} & (1)\end{matrix}$

The raw voltage measurements in this matrix reflect the properties ofthe formation as seen by the tool in the borehole. In a deviatedborehole (i.e., formation with relative dips), the raw measurements areinfluenced by the relative dips and/or strikes, which may complicatedata processing. In this situation, it is desirable to rotate thismatrix into a more convenient coordinate system before data analysis.For example, U.S. Pat. No. 6,584,408 issued to Omeragic discloses amethod that converts a complete set of couplings between thetransmitters and receivers of a triaxial system between a formationcoordinate system and a tool coordinate system. The conversionsimplifies the data processing and allows for a direct inversion of themeasurements for horizontal and vertical conductivity and dip and strike(dip-azimuthal) angles.

The voltages received by an axial receiver from energizing the triaxialtransmitter may be represented as a 3-element vector:[V_(xx)V_(xx)V_(xx)]  (2)

The triaxial and axial measurements obtained with a tool of theinvention may be analyzed (by inversion) using a proper formation modelto derive the formation electrical parameters. The modeling may use anysuitable programs known in the art. Examples of such programs includethose disclosed in Anderson, et al., “The Response of Induction Tools toDipping Anisotropic Formations, ” Transactions of the SPWLA 36th AnnualLogging Symposium, Paris, France, Jun. 26–29, 1995, paper D, Anderson etal., “The effect of crossbedding anisotropy on induction tool response,” presented at the SPWLA 39th Annual Logging Symposium, May 26–29, 1998,Keystone, Colo., Paper B, and Davydycheva, et al., “An efficientfinite-difference scheme for electro-magnetic logging in 3D anisotropicinhomogeneous media, ” Geophysics, Vol. 68, No. 5 (September–October2003), p. 15251536.

FIG. 9 shows a flow chart depicting a method 900 for deriving formationresistivity properties from the axial and triaxial measurements. First aformation model is defined (shown as 92). This involves choosing aproper formation model, defining bed boundaries in the formation model,and determining some initial formation property estimates. This processmay rely on data obtained from induction log, e.g., the triaxialinduction data (shown as 91), and formation information available fromother logs or other information about the formation such as, but notlimited to, seismic data, mud logging or drilling data (shown as 93).

Formation models that are commonly used to determine formationresistivity include 1D model, 1D+1D model, 2D model, and 3D model. FIG.10 shows a 1D model, in which the resistivity varies with radialdistance (r) from the wellbore. An alternative 1D model (not shown)involves resistivity variation as a function of the vertical distance(z). If the formation resistivity varies independently in both theradial (r) and vertical (z) directions, it may be modeled with a 1D+1Dmodel (not shown). If the radial variations (e.g., mud invasion fronts)are different in different sedimentation layers, then a 2D formationmodel shown in FIG. 11 may be used. If the well is deviated, then a 3Dmodel may be necessary (FIG. 12).

Before modeling, the various couplings from each array may be correctedfor borehole effects, shoulder effects, skin effects, and verticalresolution mismatches using any method known in the art. For example,the triaxial Grimaldi processing disclosed in U.S. Pat. No. 6,216,089 B1issued to Minerbo and U.S. Pat. No. 6,304,086 B1 issued to Minerbo etal. may be used to correct for shoulder effects and vertical resolutionmismatches in the log data. This processing yields a log of estimates ofR_(v) and R_(h) with a depth of investigation defined by the Grimaldispacing. Inverting this estimate using the radial responses in a 1Dradial formation model (FIG. 10) or a 1D+1D model will produce estimatesof the true formation anisotropic resistivity. For formations that the1D+1D inversion is not sufficient, 2D or 3D inversions may be used.

Once a basic formation model is chosen, the formation parameters may beestimated by inverting the log data. A formation model is typicallydefined as a sequence of parallel layers. The first step of theinversion involves estimating bed boundary positions. Detection of thebed boundaries from the log data may be performed, for example, by asegmentation algorithm, which identifies and positions boundaries on aselected set of logs. A simple logic can be used to distinguish betweeninvaded and un-invaded beds, based on a user-defined invasion flag,triggered from any log. The output of this task is a formation modeldescribed by a limited set of parameters: bed boundaries, horizontal andvertical resistivities for both the invaded and the virgin zone, and theinvasion radius (see FIGS. 10–12).

The inversion process involves minimizing a cost function (or penaltyfunction) C(p). An example of a cost (penalty) function may be definedas a weighted squared difference between the selected measurements andthe corresponding modeled logs:

$\begin{matrix}{{{C(p)} = {\sum\limits_{i}^{\;}\;{a_{i}\frac{{{M_{i} - {f_{i}(p)}}}^{2}}{\mu_{i}^{2}}}}},} & (3)\end{matrix}$where p is the unknown parameter vector (resistivities or geometricalparameters), M_(i) is a measurement channel, f_(i) is the correspondingtheoretical tool response computed by a forward model, □_(i) is theestimation of the confidence on measurement M_(i), and a_(i) auser-selected weight. The weight a_(i), for example, can be used todecrease the influence of shallow array measurements in poor boreholeconditions or unfavorable mud resistivity contrast for the tool. Thesummation in equation (3) may be performed on all tool measurements,i.e., measurements obtained by the axial arrays, triaxial arrays, andthe electrode devices, if present. The inversion is an iterativeprocess, which is terminated when the cost function is below aconvergence criterion. In addition, various penalty functions can beadded to the expression in equation 3 to stabilize the solution. Thesepenalty functions can have a wide range of forms, but generally theyserve to penalize formations with large variations in parameters orformations that vary greatly from geologically preferred models.

Referring to FIG. 9 again, once a formation model is defined, a forwardmodel then computes the theoretical response of the tool to thisformation model (step 94) and compares it with the actual measurements(step 96). If a significant mismatch occurs between the two (i.e., highcost function), the formation property values are refined (step 97) toreduce the difference. These processes are repeated until the matchbecomes acceptable with respect to specific convergence criteria. If thecomputed logs match the field data, then the modeling is terminated andthe formation properties are output as formation logs (step 98). Theoutput properties may include invasion profiles (e.g., radii ofinvasion), invasion zone resistivity (either isotropic resistivity,R_(xo), or anisotropic resistivities, R_(xo,v) and R_(xo,h)), andformation resistivity (either isotropic resistivity, R_(t), oranisotropic resistivities, R_(v) and R_(h)).

The above described modeling process may also provide an indicator ofthe quality of the parameter estimates. A quality control indicator istypically based on the values of the cost function or the individual logreconstruction errors. For example, a quality indicator may be definedas the difference between the measured values and the computed values asa percentage of the computed values:

$\begin{matrix}{{{Re}\mspace{11mu} c_{i}} = {100 \times \frac{\left\lbrack {M_{i} - {f_{i}(p)}} \right\rbrack}{f_{i}(p)}}} & (4)\end{matrix}$

The above described inversion and modeling may be applied to any logdata obtained using a tool in accordance with the invention. The method900 shown in FIG. 9 is generally applicable regardless of formationdips, anisotropy, or invasion. Thus, the method in combination with atool of the invention may be used to determine formation electricalproperties regardless of mud invasion or formation anisotropy. Themethod can be implemented as a program stored on the electronic module(e.g., 201 in FIG. 2) of the induction tool or in a surface computer(e.g., 110 in FIG. 1).

The advantages afforded by embodiments of the present invention mayinclude the following. Embodiments of the invention provide inductiontools that can be used to provide sufficient measurements for derivingformation resistivities regardless of the extent of mud invasion and/orformation anisotropy. Because of this versatility, accuratedetermination of formation resistivities can be accomplished in anygeographic region and in any borehole environment. Embodiments of theinvention may be used in a wireline or an MWD/LWD tool. In addition,embodiments of the invention may be used in wells drilled withwater-based mud or oil-based mud. A tool in accordance with theinvention includes both axial and triaxial arrays, which have a commontriaxial transmitter. This simplifies the tool configuration andimproves manufacturing and operating efficiencies.

While the invention has been described with respect to a limited numberof embodiments, those skilled in the art, having benefit of thisdisclosure, will appreciate that other embodiments can be devised whichdo not depart from the scope of the invention as disclosed herein. Forexample, an induction or propagation tool in accordance with embodimentsof the invention may comprise various combinations of axial and triaxialarrays, not just the examples shown. In addition, a tool in accordancewith embodiments of the invention may include induction arrays orpropagation arrays. Accordingly, the scope of the invention should belimited only by the attached claims.

1. A method for well logging, comprising: disposing an electromagneticlogging tool in a borehole penetrating a formation; obtaining aplurality of measurements of formation resistivity while the loggingtool is substantially at a particular location within the borehole,wherein the plurality of measurements cover at least three differentdepths of investigation and at least one of the plurality ofmeasurements is sensitive to formation anisotropy; and determining anelectrical property of the formation based on the plurality ofmeasurements.
 2. The method of claim 1, wherein the determining anelectrical property of the formation comprises determining an invadedzone resistivity, an un-invaded zone resistivity, formation anisotropy,or any combination thereof.
 3. The method of claim 2, wherein theinvaded zone resistivity comprises a horizontal resistivity and avertical resistivity.
 4. The method of claim 2, wherein the un-invadedzone resistivity comprises a horizontal resistivity and a verticalresistivity.
 5. The method of claim 1, wherein the plurality ofmeasurements comprise at least one galvanic measurement.
 6. The methodof claim 1, wherein the determining an electric property of theformation uses a formation model selected from a 1D model, a 1D+1Dmodel, a 2D model, and a 3D model.